Render of Planet Earth in Blender Render and Cycles
Cycles is capable of utilizing physically-based rendering techniques, but that doesn't inherently make every render appear photo-realistic. See How is Cycles different from Blender Internal?

To get a nice atmospheric scattering effect in cycles, I'd suggest wrapping your earth sphere in a slightly-larger sphere with a volumetric material such as this: 



Result:



Note that these values are arbitrarily hand-picked based on what I thought "looked nice". If you are after accuracy you'll probably want to do a bit more research than I did ;)

It could use some tweaking, but it does look somewhat similar to actual photographs of the earth:

 

Note that in the above setup the atmosphere is a constant density. The real atmosphere gets less dense higher up, creating a subtle falloff. This is pretty easy to simulate with a spherical gradient texture, but will vastly increase render time.  



If you don't see the edge of the atmosphere very close up in your render, simulating this may not be necessary.



In response to the edits to the question:

To get rid of the grid-like pattern, add a subsurf modifier to the atmosphere sphere and increase the number of subdivisions until it's no longer apparent.

The reason the earths atmosphere appears bluer at the edges is because light which travels farther through the atmosphere is more likely to be scattered off air molecules. Since rays closer the edge of the atmosphere which travel farther through it, they appear bluer:



Keep in mind that thickness matters a lot with volume rendering, so another thing you can tweak (in addition to the density etc.) is the scale of the atmosphere object (adding more or less atmosphere on top of the ground)

Here's the .blend of my setup:


Textures intentionally omitted

Note that everything is just eyeballed; nothing is based on real-world data.